We report a system where fixed interactions between noncomputational levels make bright the otherwise forbidden two-photon $|00⟩\to |11⟩$ transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces two-photon Rabi-like oscillations between the ground and doubly excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of $F_g=90\%$ (unconstrained) and 86% (maximum likelihood estimator).

For extremely confined fluids with a two-dimensional density $n$ in slit geometry of an accessible width $L$, we prove that in the limit $L\to 0$, the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For a small wall separation, the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify $n{L}^2$ as the hidden smallness parameter of the confinement problem and evaluate the effective two-body potential analytically, which allows calculating the leading correction to the free energy exactly. Explicitly, we map a fluid of hard spheres in extreme confinement onto a 2D fluid of disks with an effective hard-core diameter and a soft boundary layer. Two-dimensional phase transitions are robust and the transition point experiences a shift $\mathcal{O}(n{L}^2)$.

A three-component Fermi gas near a broad Feshbach resonance does not have a universal ground state due to the Thomas collapse, while it does near a narrow Feshbach resonance. We explore its universal phase diagram in the plane of the inverse scattering length $1/a{k}_F$ and the resonance range $R_{*}{k}_F$. For a large $R_{*}{k}_F$, there exists a Lifshitz transition between superfluids with and without an unpaired Fermi surface as a function of $1/a{k}_F$. With decreasing $R_{*}{k}_F$, the Fermi surface coexisting with the superfluid can change smoothly from that of atoms to trimers (“atom-trimer continuity”), corresponding to the quark-hadron continuity in a dense nuclear matter. Eventually, there appears a finite window in $1/a{k}_F$ where the superfluid is completely depleted by the trimer Fermi gas, which gives rise to a pair of quantum critical points. The boundaries of these three quantum phases are determined in regions where controlled analyses are possible and are also evaluated based on a mean-field plus trimer model.

A localized qubit entangled with a propagating quantum field is well suited to study nonlocal aspects of quantum mechanics and may also provide a channel to communicate between spatially separated nodes in a quantum network. Here, we report the on-demand generation and characterization of Bell-type entangled states between a superconducting qubit and propagating microwave fields composed of zero-, one-, and two-photon Fock states. Using low noise linear amplification and efficient data acquisition we extract all relevant correlations between the qubit and the photon states and demonstrate entanglement with high fidelity.

We demonstrate feedback control of a superconducting transmon qubit using discrete, projective measurement and conditional coherent driving. Feedback realizes a fast and deterministic qubit reset to a target state with 2.4% error averaged over input superposition states, and allows concatenating experiments more than 10 times faster than by passive initialization. This closed-loop qubit control is necessary for measurement-based protocols such as quantum error correction and teleportation.

Quantum walks have by now been realized in a large variety of different physical settings. In some of these, particularly with trapped ions, the walk is implemented in phase space, where the corresponding position states are not orthogonal. We develop a general description of such a quantum walk and show how to map it into a standard one with orthogonal states, thereby making available all the tools developed for the latter. This enables a variety of experiments, which can be implemented with smaller step sizes and more steps. Tuning the nonorthogonality allows for an easy preparation of extended states such as momentum eigenstates, which travel at a well-defined speed with low dispersion. We introduce a method to adjust their velocity by momentum shifts, which allows us to experimentally probe the dispersion relation, providing a benchmarking tool for the quantum walk, and to investigate intriguing effects such as the analog of Bloch oscillations.

The number of four-body states known to behave universally is small. This work adds a new class of four-body states to this relatively short list. We predict the existence of a universal four-body bound state for heavy-light mixtures consisting of three identical heavy fermions and a fourth distinguishable lighter particle with a mass ratio $\kappa \gtrsim 9.5$ and short-range interspecies interaction characterized by a positive $s$-wave scattering length. The structural properties of these universal states are discussed, and finite-range effects are analyzed. The bound states can be experimentally realized and probed by utilizing ultracold atom mixtures.

A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the space of density matrices corresponding to the fixed points of the dynamics are identified, and the existence of a transition between the phase in which gain and loss are balanced and the phase in which this balance is lost is illustrated in terms of the time average of observables. The model is extended to include a noise term that results from a uniform random perturbation generated by white noise. Numerical studies of example systems show the emergence of equilibrium states that suppress the phase transition.

Blind quantum computation is a secure delegated quantum computing protocol where Alice, who does not have sufficient quantum technology at her disposal, delegates her computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice’s input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qudit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-Lieb-Tasaki model, and the Raussendorf-Harrington-Goyal topological model. Here, we consider blind quantum computation for the continuous-variable measurement-based model. We show that blind quantum computation is possible for the infinite squeezing case. We also show that the finite squeezing causes no additional problem in the blind setup apart from the one inherent to the continuous-variable measurement-based quantum computation.

Many-particle optical lattice clocks have the potential for unprecedented measurement precision and stability due to their low quantum projection noise. However, this potential has so far never been realized because clock stability has been limited by frequency noise of optical local oscillators. By synchronously probing two ${}^{87}\mathrm{Sr}$ lattice systems using a laser with a thermal noise floor of $1\times {10}^{-15}$, we remove classically correlated laser noise from the intercomparison, but this does not demonstrate independent clock performance. With an improved optical oscillator that has a $1\times {10}^{-16}$ thermal noise floor, we demonstrate an order of magnitude improvement over the best reported stability of any independent clock, achieving a fractional instability of $1\times {10}^{-17}$ in 1000 s of averaging time for synchronous or asynchronous comparisons. This result is within a factor of 2 of the combined quantum projection noise limit for a 160 ms probe time with $\sim {10}^3$ atoms in each clock. We further demonstrate that even at this high precision, the overall systematic uncertainty of our clock is not limited by atomic interactions. For the second Sr clock, which has a cavity-enhanced lattice, the atomic-density-dependent frequency shift is evaluated to be $-3.11\times {10}^{-17}$ with an uncertainty of $8.2\times {10}^{-19}$.

We evaluated the $C_6$ coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, $C_6=1929(39)\mathrm{a}.\mathrm{u}.$, is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb $6s^2{}^{1}S_0-6s6p{}^{3}P_0^o$ clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the ${10}^{-18}$ level.

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for these weak values within the reduced system Hilbert space. As an application of the approach, we show that for any Hermite-Gauss mode of a paraxial beamlike detector these expressions reduce to the real and imaginary parts of a single system weak value plus an additional weak-value-like contribution that only affects the momentum shift.

We report the measurement of the anisotropic ac polarizability of ultracold polar ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a “magic” angle between the laser polarization and the quantization axis is found where the polarizability of the $|N=0,m_N=0⟩$ and the $|N=1,m_N=0⟩$ states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the coherence time. This paves the way for precise spectroscopic measurements and coherent manipulations of rotational states as a tool in the creation and probing of novel quantum many-body states of polar molecules.

Entanglement is typically created via systematic intervention in the time evolution of an initially unentangled state, which can be achieved by coherent control, carefully tailored nondemolition measurements, or dissipation in the presence of properly engineered reservoirs. In this Letter we show that two-component Fermi gases at $\sim \mu \mathrm{K}$ temperatures naturally evolve, in the presence of reactive two-body collisions, into states with highly entangled (Dicke-type) spin wave functions. The entanglement is a steady-state property that emerges-without any intervention-from uncorrelated initial states, and could be used to improve the accuracy of spectroscopy in experiments with fermionic alkaline earth atoms or fermionic ground state molecules.

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

We introduce a generalized Hamiltonian mean field model—an $XY$ model with both linear and quadratic coupling between spins and explicit Hamiltonian dynamics. In addition to the usual paramagnetic and ferromagnetic phases, this model also possesses a nematic phase. The generalized Hamiltonian mean field model can be solved explicitly using Boltzmann-Gibbs statistical mechanics, in both canonical and microcanonical ensembles. However, when the resulting microcanonical phase diagram is compared with the one obtained using molecular dynamics simulations, it is found that the two are very different. We will present a dynamical theory which allows us to explicitly calculate the phase diagram obtained using molecular dynamics simulations without any adjustable parameters. The model illustrates the fundamental role played by dynamics as well the inadequacy of Boltzmann-Gibbs statistics for systems with long-range forces in the thermodynamic limit.

We observe matter wave interference of a single cesium atom in free fall. The interferometer is an absolute sensor of acceleration and we show that this technique is sensitive to forces at the level of $3.2\times {10}^{-27}\mathrm{N}$ with a spatial resolution at the micron scale. We observe the build up of the interference pattern one atom at a time in a free-space interferometer where the mean path separation extends far beyond the coherence length of the atom. Using the coherence length of the atom wave packet as a metric, we directly probe the velocity distribution and measure the temperature of a single atom in free fall.

By selectively probing the center of a trapped gas, we measure the local, or homogeneous, contact of a unitary Fermi gas as a function of temperature. Tan’s contact, $C$, is proportional to the derivative of the energy with respect to the interaction strength and is thus an essential thermodynamic quantity for a gas with short-range correlations. Theoretical predictions for the temperature dependence of $C$ differ substantially, especially near the superfluid transition, $T_c$, where $C$ is predicted to either sharply decrease, sharply increase, or change very little. For $T/T_F>0.4$, our measurements of the homogeneous gas contact show a gradual decrease of $C$ with increasing temperature, as predicted by theory. We observe a sharp decrease in $C$ at $T/T_F=0.16$, which may be due to the superfluid phase transition. While a sharp decrease in $C$ below $T_c$ is predicted by some many-body theories, we find that none of the predictions fully account for the data.

One of the principal models of magnetic sensing in migratory birds rests on the quantum spin dynamics of transient radical pairs created photochemically in ocular cryptochrome proteins. We consider here the role of electron spin entanglement and coherence in determining the sensitivity of a radical pair-based geomagnetic compass and the origins of the directional response. It emerges that the anisotropy of radical pairs formed from spin-polarized molecular triplets could form the basis of a more sensitive compass sensor than one founded on the conventional hyperfine-anisotropy model. This property offers new and more flexible opportunities for the design of biologically inspired magnetic compass sensors.